On an extremal problem in “investment–consumption” models

In the «investment–consumption» model, the growth rate of capital-labor ratio is the difference between own investments and the rate of depreciation. If there is a goal to achieve a given level of capital-labor ratio by a fixed point in time, but own investment is not enough for this, it is necessary to attract additional funds that come in the form of financial flow. The amount of flow is limited from above by the function — the ultimate ability to absorb investments. The article provides an answer to the question of what is the minimum amount of additional funds and in the form of what financial flow they must arrive in order for the goal to be achieved. It turns out that the desired flow is arranged as follows. There is a pair of capital-labor ratio values between the initial and target values such that as long as the capital-labor ratio varies from the lower to the higher value, only own investment is used. The rest of the time, additional funds are used at the maximum possible pace. Formulas for calculating the specified values of capital-labor ratio, as well as a formula for calculating the amount of additional funds have been obtained.